mlsanityData to 14 Oct 2026

Control, Optimal Transport and Neural Differential Equations in Supervised Learning

arXiv 2503.15105 ↗First posted 19 Mar 2025math.NA cs.LG cs.NAcited by 1

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Abstract (arXiv)

We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal transport (UOT) in the continuum using Neural ODEs. By generalizing a discrete UOT problem with Pearson divergence, we constructively design vector fields for Neural ODEs that converge to the true UOT dynamics, thereby advancing the mathematical foundations of computational transport and machine learning. To this end, we design a numerical scheme inspired by the Sinkhorn algorithm to solve the corresponding minimization problem and rigorously prove its convergence, providing explicit error estimates. From the obtained numerical solutions, we derive vector fields defining the transport dynamics and construct the corresponding transport equation. Finally, from the numerically obtained transport equation, we construct a neural differential equation whose flow converges to the true transport dynamics in an appropriate limiting regime.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 43 of its 94 references that are in the map. First posted on arXiv 19 Mar 2025.

Builds on

43 of 94 references.

References · 43

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31 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Accelerated Sinkhorn Algorithms for Partial Optimal Transportcited by 0